This document presents an agenda for a talk on Petri nets. It begins with an introduction to Petri nets that defines their structure, including places, transitions, tokens, and firing rules. It then discusses several analysis methods for Petri nets, including reachability trees, incidence matrices, and reduction rules. Next, it covers high-level Petri nets and colored Petri nets. The document concludes by mentioning an application of Petri nets to rumor detection and blocking in online social networks, and introduces orbital Petri nets as a promising approach.
Problem solving
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Defining a Search Problem
State Space Graph versus Search Trees
Graph vs. Tree
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Problem solving
Problem formulation
Search Techniques for Artificial Intelligence
Classification of AI searching Strategies
What is Search strategy ?
Defining a Search Problem
State Space Graph versus Search Trees
Graph vs. Tree
Problem Solving by Search
In this PDF you will find the basics of Turbo Prolog 2.0 with some good program and it's output. Also it's second part is coming in next month or week.
For any query ------------------> sohupatel8828@gmail.com
For programs ----------------> https://github.com/UltraHopeful/Turbo-Prolog-2.0
Credit : Nusrat Jahan & Fahima Hossain , Dept. of CSE, JnU, Dhaka.
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In this PDF you will find the basics of Turbo Prolog 2.0 with some good program and it's output. Also it's second part is coming in next month or week.
For any query ------------------> sohupatel8828@gmail.com
For programs ----------------> https://github.com/UltraHopeful/Turbo-Prolog-2.0
Credit : Nusrat Jahan & Fahima Hossain , Dept. of CSE, JnU, Dhaka.
Randomized Algorithm- Advanced Algorithm, Deterministic, Non Deterministic, LAS Vegas, MONTE Carlo Algorithm.
How can you deal with Fuzzy Logic. Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. In contrast with traditional logic theory, where binary sets have two-valued logic: true or false, fuzzy logic variables may have a truth value that ranges in degree
between 0 and 1
Knowledge representation and Predicate logicAmey Kerkar
This presentation is specifically designed for the in depth coverage of predicate logic and the inference mechanism :resolution algorithm.
feel free to write to me at : amecop47@gmail.com
Mathematical support for preventive maintenance periodicity optimization of r...Alexander Lyubchenko
The work is aimed to present an approach for estimation of recommended maintenance intervals of radiocommunication devices which is based on the developed Monte Carlo simulation model and the suggested optimality criterion for calculation of the rational periodicity on the basis of obtained values of reliability indexes. The model takes into account the following exploitation factors: sudden, gradual, latent and fictitious failures, human factor of service staff and time parameters of preventive maintenance. The suggested mathematical support allows providing of the high reliability of the exploited equipment.
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In the classical model, the fundamental building block is represented by bits exists in two states a 0 or a 1. Computations are done by logic gates on the bits to produce other bits. By increasing the number of bits, the complexity of problem and the time of computation increases. A quantum algorithm is a sequence of operations on a register to transform it into a state which when measured yields the desired result. This paper provides introduction to quantum computation by developing qubit, quantum gate and quantum circuits.
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For more details visit on YouTube; @SELF-EXPLANATORY;
https://www.youtube.com/channel/UCAiarMZDNhe1A3Rnpr_WkzA/videos
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Spectroscopy is a branch of science dealing the study of interaction of electromagnetic radiation with matter.
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Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
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Involved in silencing mRNA transcripts.
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1. SRGE
1
Petri Nets: Properties, Analysis and
Applications
Presented By
Dr. Mohamed Torky
PHD in Computer Science (2018), Faculty of Science, Menoufyia University, Egypt.
Member in Scientific Research Group in Egypt (SRGE)
2. Agenda
2
1
• What is Petri Nets ?
2
• Analysis Methods of Petri Nets
3
• High Level Petri Nets
4
• Petri Nets Application: Rumor Detection and Blocking in OSN
5
• Orbital Petri Nets : A Promising Petri Net Approach
3. Agenda
3
1
• What is Petri Nets ?
2
• Analysis Methods of Petri Nets
3
• High Level Petri Nets
4
• Petri Nets Application: Rumor Detection and Blocking in OSN
5
• Orbital Petri Nets : A Promising Petri Net Approach
5. 8/12/2018
1- What is Petri Nets ?
(Transition, Enabling, and Firing Rules)
P1
P2
P3
t1
2
3
𝑴 𝟎 = (𝟐, 𝟐, 𝟎 )
𝑴 𝟏 = (𝟎, 𝟏, 𝟑 )
6. 1- What is Petri Nets ?
(Petri Net Structure)
t1 t2 t3
t1
t2 t3
t4 t5
(A sequence Structure)
(Concurrent Structure)
7. 1- What is Petri Nets ?
(Petri Net Structure)
(Synchronization Structure)
t1
8. 1- What is Petri Nets ?
(Petri Net Structure)
(Synchronization and Concurrency Structure)
t1
9. 1- What is Petri Nets ?
(Example: computation of X=(a+b)/(a-b)
t6
t2
t3
t4
t5
t1
t7
P2
P1
P3
P4
P5
P6
P7
P8
P9
Add
Subtract
If (a-b≠0)
If (a-b=0)
Divide X=(a+b)/(a-b)=3a=8
a=8
b=4
b=4
a+b=12
a-b=4
X=Undefined
a-b=4
10. 1- What is Petri Nets ?
(Petri Net Properties )
Structure Properties Behavior Properties
11. 1- What is Petri Nets ?
(Behavior Properties)
Reachability
Boundness
Liveness
Reversibility
Coverability
Persistence
Fairness
Behavioral properties of a Petri net
depend on the initial marking and the
firing policy , so it sometimes called
Marking-dependent properties. These
properties are thus of great
importance when designing dynamic
systems , hence, it depends on the
behavior of the system not its
structure.
12. 1- What is Petri Nets ?
(Behavior Properties)
Reachability: A Marking 𝑴 𝒏 is said to
Reachable from the initial marking 𝑴 𝟎 if
there exists a firing sequence
𝝈{𝒕𝟏, 𝒕𝟐, 𝒕𝟑, … 𝒕𝒏} that transform𝑴 𝟎 to 𝑴 𝒏
(i.e. 𝑴 𝒏 𝝐 𝑹(𝑴 𝟎) )
Reachability Graph
13. 1- What is Petri Nets ?
(Behavior Properties)
Boundness: A Petri net is said to be K-bounded if
the number of tokens in each place doesn't
exceed a finite number K for any marking 𝑴𝒏
reachable from 𝑴𝟎 (i.e. 𝑴(𝑷) ≤ 𝑲)
𝑴(𝑷𝒊) ≤ 𝟐
𝑴(𝑷𝒊) ≤ 𝟏
14. 1- What is Petri Nets ?
(Behavior Properties)
Reversibility: A Petri net (𝑵, 𝑴𝟎) is said to be reversible if
for each marking 𝑴 𝝐 𝑹(𝑴𝟎), 𝑴𝟎 is Reachable From M. A
marking M” is said to be a Home State if for each marking
𝑴 𝝐 𝑹(𝑴𝟎), M” is Reachable from M
Reachability GraphReversible Net
15. 1- What is Petri Nets ?
(Behavior Properties)
Presistence: A Petri net is said to be
persistent if, for any two enabled transitions,
occurrence of one transition will not disable
another.
Persistent Net
16. 1- What is Petri Nets ?
(Behavior Properties)
Fairness: A Petri net (𝑵. 𝑴𝟎) is said to be 𝑩
− 𝒇𝒂𝒊𝒓 net if, every pair of transitions in the net
are in a B-fair relation. i.e. every transition in the
net appear infinitely in a finite sequence of
transitions
B-Fair Net
17. 1- What is Petri Nets ?
(Structure Properties)
Structure properties of depend only on its
structure, and not on the initial marking
and the firing policy. These properties are
thus of great importance when designing
static systems, since they depend only on
the layout, and not on the way the system
will be behave, Most of the structural
properties can be easily verified by means
of algebraic techniques.
18. Agenda
18
1
• What is Petri Nets ?
2
• Analysis Methods of Petri Nets
3
• High Level Petri Nets
4
• Petri Nets Application: Rumor Detection and Blocking in OSN
5
• Orbital Petri Nets : A Promising Petri Net Approach
22. 2-2. Incidence Matrix
Incidence Matrix: for a Petri Net (𝑵. 𝑴𝟎) with
n Transitions and m Places , the Incidence
Matrix 𝑨 = [𝒂 𝒊𝒋] is (𝒏 𝒙 𝒎) matrix of integers
as:
)1(
ijijij aaa
),( jiij ptwa
),( ijij tpwa
Where,
23. 2-2. Incidence Matrix
For The marking states which result from
transitions firing can be Expressed in the
following Equation which called State Equation:
Where,
)2(,3,2,1,1 kuAMM k
T
kk
Such that M is the marking state and A is the
incidence Matrix, and u is firing sequence vector
(u1, u2, u3,…..)
24. 2-2. Incidence Matrix
The Necessary Reachability Condition:
Suppose that the destination marking state
is 𝑴 𝒅 is reachable from 𝑴𝟎 through the firing
sequence 𝒖 = (𝒖𝟏, 𝒖𝟐, 𝒖𝟑, … … , 𝒖𝒅) . The State
equation can be rewritten as:
)3(,3,2,1,
1
0
kuAMM
d
k
k
T
d
25. 2-2. Incidence Matrix
Example (1) : given the following 𝑷𝑵 = (𝑵, 𝑴𝟎),
such that 𝑴 𝟎 = (𝟐, 𝟎, 𝟏, 𝟎),
Does the marking State 𝑴𝟏 = (𝟑, 𝟎, 𝟎, 𝟐)
is reachable from 𝑴 𝟎 ???
)1(
220
101
011
112
T
A
The Incidence Matrix
)2(,3,2,1,
1
0
kuAMM
d
k
k
T
d
Solution:
)3(.
220
101
011
112
0
1
0
2
2
0
0
3
3
2
1
u
u
u )4(
1
0
0
.
220
101
011
112
0
1
0
2
2
0
0
3
)5()2,0,0,3()0,1,0,2( 1
)1,0,0(
0
MM u
30. Agenda
30
1
• What is Petri Nets ?
2
• Analysis Methods of Petri Nets
3
• High Level Petri Nets
4
• Petri Nets Application: Rumor Detection and Blocking in OSN
5
• Orbital Petri Nets : A Promising Petri Net Approach
32. 3.1. High Level Petri Nets (HLPN)
(Enabling, Firing Rule)
t1 can be enabled in the following Modes
(1,3), (1,4), (1,5), (1,7), (3,4), (3,5), (3,7)
(x , y)
33. 3.1. High Level Petri Nets (HLPN)
(Enabling, Firing Rule)
Firing modes of t1:
𝑴 𝒑𝟏 = 𝟏’𝟏 + 𝟏’𝟑
𝑴(𝒑𝟐) = 𝟏’𝟓
𝟏 𝟑 𝟑
Mode 1: 1’(3,5)
37. 3.3. Timing Petri Nets
Definition (𝑻𝑷𝑵, 𝑴𝟎). A net is a tuple 𝑻𝑷𝑵 = (𝑷, 𝑻, 𝑰, 𝑶, 𝑻𝑺, 𝑫 ) where:
• 𝑷 = {𝑝1, 𝑝2, … 𝑝𝑛} 𝑠𝑒𝑡 𝑜𝑓 𝑝𝑙𝑎𝑐𝑒𝑠
• 𝑻 = {𝑡1, 𝑡2, 𝑡3, … . 𝑡𝑚} 𝑠𝑒𝑡 𝑜𝑓 𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑜𝑛𝑠
• 𝑰 = 𝑡ℎ𝑒 𝑠𝑒𝑡 𝑜𝑓 𝑖𝑛𝑝𝑢𝑡 𝑝𝑙𝑎𝑐𝑒𝑠 𝑡𝑜 𝑒𝑎𝑐ℎ 𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑜𝑛
• 𝐎 = the set of output places to each transition
• 𝑻𝑺 = 𝑇𝑖𝑚𝑒𝑆𝑒𝑡 :
• 𝑫 = D:T TS is the a function that define the firing delay of each transition
40. Agenda
40
1
• What is Petri Nets ?
2
• Analysis Methods of Petri Nets
3
• High Level Petri Nets
4
• Petri Nets Application: Rumor Detection and Blocking in OSN
5
• Orbital Petri Nets : A Promising Petri Net Approach
41. 4.Petri Nets Applications
41
(1) Modeling Distributed Software
System
(2) Diagnosis ( Artificial Intelligence)
(3) Discrete Process Control
(4) Operating Systems
(5) Neural Networks Applications
(6) Processing Information in OSNs
42. 4.1. Rumors Detection and Blocking in OSNs
42
Colored PN Model for Detecting and Blocking Rumors in OSNs
45. 4.2. Reachability Analysis
45
Theorem Given a Colored Petri Net model(𝐶𝑃𝑁𝑀, 𝑀0) with an initial marking
𝑴 𝟎 = (𝒏, 𝟎, 𝟎, 𝟎, 𝟎, 𝟎, 𝟎, 𝟎, 𝟎, 𝟎) With knowing the
variables 𝑛, 𝑛1. 𝑛2, 𝑛3, 𝑛4, 𝑛5, and 𝑛6 such that, 𝑛 = 𝑛1 + 𝑛2, 𝑛1 = 𝑛3 + 𝑛4, 𝑎𝑛𝑑
, 𝑛2 = 𝑛5 + 𝑛6, then the following points can be proved:
𝟏 𝑴 𝟑 ∈ 𝑹(𝑴 𝟎) , such that 𝑀3 = (0,0,0,0,0,0,0, 𝑛3 + 𝑛5, 𝑛4 + 𝑛6, 0)
𝟐 𝑴 𝟒 ∈ 𝑹(𝑴 𝟎) , such that 𝑀4 = (0,0,0,0,0,0,0, 𝑛3 + 𝑛5,0,0)
𝟑 𝑴 𝟓 ∈ 𝑹(𝑴 𝟎) , such that 𝑀5 = (0,0,0,0,0,0,0,0,0, 𝑛3 + 𝑛5)
where,
𝒏 is the number of all input tokens in Place 𝑷 𝟏,
𝒏𝟏 is the number of all tokens forward to the Place 𝑷 𝟐 and
𝒏𝟐 is the number of all tokens forward to Place 𝑷 𝟑.
𝒏𝟑 is the number of tokens forward to Place 𝑷 𝟒.
𝒏𝟒 is the number of tokens forward to Place 𝑷 𝟓
𝒏𝟓 is the number of tokens forward to Place 𝑷 𝟔 , and
𝒏𝟔 is the number of tokens forward to Place 𝑷 𝟕.
46. Agenda
46
1
• What is Petri Nets ?
2
• Analysis Methods of Petri Nets
3
• High Level Petri Nets
4
• Petri Nets Application: Rumor Detection and Blocking in OSN
5
• Orbital Petri Nets : A Promising Petri Net Approach